# Question #b7f35

Jul 13, 2016

We know that kinetic energy in Newtonian mechanics is given by the expression

$K E = \frac{1}{2} m {v}^{2}$ .......(1)
Keeping the mass $m$ constant and tripling the velocity $v$ changes the kinetic energy of the body to
$K {E}_{\text{new}} = \frac{1}{2} m {\left(3 v\right)}^{2}$
$\implies K {E}_{\text{new}} = \frac{1}{2} m \times 9 {v}^{2}$
This can be rewritten as
$\implies K {E}_{\text{new}} = 9 \times \left(\frac{1}{2} m {v}^{2}\right)$
Recognizing that quantity within the brackets is the original $K E$ as in equation (1), we may write it as
$K {E}_{\text{new}} = 9 \times K E$

$\implies$ New Kinetic energy is nine times the original kinetic energy.